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Exam 8: Rotational Equilibrium and Rotational Dynamics: Part A

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Question 1

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A 0.12-m radius grinding wheel takes 2.1 s to speed up from 2.0 rad/s to 11.0 rad/s.What is the wheel's average angular acceleration?

A) 9.6 rad/s²
B) 4.3 rad/s²
C) 1.6 rad/s²
D) 0.33 rad/s²

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Question 2

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A meterstick is supported by a knife-edge at the 50-cm mark.Doug hangs masses of 0.40 and 0.60 kg from the 35-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.30 kg to keep the stick balanced?

A) 20 cm
B) 70 cm
C) 30 cm
D) 10 cm

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D

Question 3

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A non-uniform rod of length L and mass M is pivoted about one end.The moment of inertia of this rod about its pivoted end is ) Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass 2M.What is the moment of inertia of this configuration about the pivot?

A 0.40-m radius automobile tire accelerates from rest at a constant 2.0 rad/s².What is the centripetal acceleration of a point on the outer edge of the tire after 5.0 s?

A 4.0-kg mass is placed at (3.0,4.0) m,and a 7.0 kg-mass is placed at (3.0,−4.0) m.What is the moment of inertia of this system of masses about the z axis?

Which of the first units given below can be units for angular acceleration while the second units can be units for angular velocity?

A woman who weighs 500 N stands on an 8.0 m long board that weighs 100 N.The board is supported at each end.The support force at the right end is 2 times the support force at the left end.How far from the right end is the woman standing?

A spool of thread has an average radius of 1.00 cm.If the spool contains 126 m of thread,how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.

A circular disk is rotating about a central axis with an angular velocity which is increasing at a constant rate.Point 1 on the disk is located at a distance From the center of the disk and point 2 on the disk is located at a distance From the center of the disk.If ,which of the following ratios is the largest? 1 and 2 refer to being at points 1 and 2 in the subscripts below,all values occurring at the same time.

A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 2.5 rad.What is its average angular acceleration?

A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m.How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.20 m/s?

A baseball pitcher loosens up his pitching arm.He tosses a 0.20-kg ball using only the rotation of his forearm,0.32 m in length,to accelerate the ball.What is the moment of inertia of the ball alone as it moves in a circular arc with a radius of 0.32 m?

A 0.200-kg object is swung in a circular path and in a vertical plane on a 0.500-m length string.If the angular speed at the bottom is 8.00 rad/s,what is the tension in the string when the object is at the bottom of the circle?

A baseball pitcher,loosening up his arm before a game,tosses a 0.15-kg ball using only the rotation of his forearm,0.32 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 24 m/s in a time of 0.40 s,what is the average angular acceleration of the arm and ball?

A bank vault is opened by applying a force of 300 N perpendicular to the plane of the door,1.2 m from the hinges.Find the torque due to this force about an axis through the hinges.

Two children seat themselves on a seesaw.The one on the left has a weight of 400 N while the one on the right weighs 300 N.The fulcrum is at the midpoint of the seesaw.If the child on the right is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced,what is the torque provided by the weight of the child on the left? (Take ccw as positive. )

A 4.0-kg mass is placed at (3.0,4.0) m,and a 7.0-kg mass is placed at (3.0,−4.0) m.What is the moment of inertia of this system of masses about the x axis?

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth,frictionless wall.If the ladder has a mass of 30 kg and it makes an angle of 60° with the ground,find the force of friction of the ground on the foot of the ladder.

A bucket filled with water has a mass of 23 kg and is attached to a rope,which in turn,is wound around a 0.080-m radius cylinder at the top of a well.What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s²)

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.4L from the left end.On the left end is placed a mass of weight 2W and on the right end a vertical force F is applied to keep the system in balance.What are the magnitude and direction of the force F?